Properties

Label 177.14.a.b.1.13
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $1$
Dimension $31$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(189.798744245\)
Analytic rank: \(1\)
Dimension: \(31\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-57.5851 q^{2} -729.000 q^{3} -4875.95 q^{4} +31633.2 q^{5} +41979.6 q^{6} +267144. q^{7} +752520. q^{8} +531441. q^{9} +O(q^{10})\) \(q-57.5851 q^{2} -729.000 q^{3} -4875.95 q^{4} +31633.2 q^{5} +41979.6 q^{6} +267144. q^{7} +752520. q^{8} +531441. q^{9} -1.82160e6 q^{10} +3.70473e6 q^{11} +3.55457e6 q^{12} +3.03857e7 q^{13} -1.53835e7 q^{14} -2.30606e7 q^{15} -3.39015e6 q^{16} +5.25313e6 q^{17} -3.06031e7 q^{18} -1.93452e8 q^{19} -1.54242e8 q^{20} -1.94748e8 q^{21} -2.13337e8 q^{22} -1.22257e8 q^{23} -5.48587e8 q^{24} -2.20043e8 q^{25} -1.74976e9 q^{26} -3.87420e8 q^{27} -1.30258e9 q^{28} +8.14387e8 q^{29} +1.32795e9 q^{30} +1.38541e9 q^{31} -5.96942e9 q^{32} -2.70075e9 q^{33} -3.02502e8 q^{34} +8.45061e9 q^{35} -2.59128e9 q^{36} -2.86691e10 q^{37} +1.11400e10 q^{38} -2.21512e10 q^{39} +2.38046e10 q^{40} -1.17360e10 q^{41} +1.12146e10 q^{42} -2.19728e10 q^{43} -1.80641e10 q^{44} +1.68112e10 q^{45} +7.04019e9 q^{46} -4.74856e10 q^{47} +2.47142e9 q^{48} -2.55232e10 q^{49} +1.26712e10 q^{50} -3.82953e9 q^{51} -1.48159e11 q^{52} -1.45553e11 q^{53} +2.23097e10 q^{54} +1.17193e11 q^{55} +2.01031e11 q^{56} +1.41026e11 q^{57} -4.68966e10 q^{58} -4.21805e10 q^{59} +1.12442e11 q^{60} -5.68197e10 q^{61} -7.97793e10 q^{62} +1.41971e11 q^{63} +3.71522e11 q^{64} +9.61197e11 q^{65} +1.55523e11 q^{66} +6.47814e11 q^{67} -2.56140e10 q^{68} +8.91254e10 q^{69} -4.86630e11 q^{70} -1.68243e11 q^{71} +3.99920e11 q^{72} -6.75444e11 q^{73} +1.65091e12 q^{74} +1.60411e11 q^{75} +9.43262e11 q^{76} +9.89696e11 q^{77} +1.27558e12 q^{78} -1.56297e11 q^{79} -1.07241e11 q^{80} +2.82430e11 q^{81} +6.75817e11 q^{82} -3.56084e12 q^{83} +9.49581e11 q^{84} +1.66173e11 q^{85} +1.26531e12 q^{86} -5.93688e11 q^{87} +2.78788e12 q^{88} -6.47668e12 q^{89} -9.68074e11 q^{90} +8.11735e12 q^{91} +5.96120e11 q^{92} -1.00997e12 q^{93} +2.73446e12 q^{94} -6.11950e12 q^{95} +4.35171e12 q^{96} -1.96982e12 q^{97} +1.46976e12 q^{98} +1.96885e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} - 3854663q^{10} + 3943968q^{11} - 92499894q^{12} - 48510022q^{13} - 51427459q^{14} - 24411294q^{15} + 370110498q^{16} + 83288419q^{17} - 27634932q^{18} - 180425297q^{19} + 753620445q^{20} + 827807931q^{21} + 2300196142q^{22} - 1305810279q^{23} + 1107897021q^{24} + 8070954867q^{25} + 464550322q^{26} - 12010035159q^{27} - 9887169562q^{28} + 6248352277q^{29} + 2810049327q^{30} - 26730150789q^{31} - 24001343230q^{32} - 2875152672q^{33} - 36571033348q^{34} + 10255900979q^{35} + 67432422726q^{36} - 43284776933q^{37} - 36293696947q^{38} + 35363806038q^{39} - 105980683856q^{40} - 9961079285q^{41} + 37490617611q^{42} - 51755851288q^{43} - 59623729442q^{44} + 17795833326q^{45} - 202287132683q^{46} - 82747063727q^{47} - 269810553042q^{48} + 535277836542q^{49} + 526974390461q^{50} - 60717257451q^{51} + 544982341446q^{52} + 561701818494q^{53} + 20145865428q^{54} - 521861534450q^{55} - 228056576664q^{56} + 131530041513q^{57} + 10555409160q^{58} - 1307596542871q^{59} - 549389304405q^{60} + 618193248201q^{61} - 1486611437386q^{62} - 603471981699q^{63} + 679062548045q^{64} - 1130583307122q^{65} - 1676842987518q^{66} - 4137387490592q^{67} - 3901389300295q^{68} + 951935693391q^{69} - 819291947844q^{70} - 3766439869810q^{71} - 807656928309q^{72} - 2386775553523q^{73} + 3060770694642q^{74} - 5883726098043q^{75} - 847741068784q^{76} + 1650423006137q^{77} - 338657184738q^{78} + 787155757766q^{79} + 13999832121779q^{80} + 8755315630911q^{81} + 10083281915577q^{82} + 8743877051639q^{83} + 7207746610698q^{84} + 15373177520565q^{85} + 18939443838984q^{86} - 4555048809933q^{87} + 39713314506713q^{88} + 11026795445259q^{89} - 2048525959383q^{90} + 23285721962531q^{91} + 40411079823254q^{92} + 19486279925181q^{93} + 35237377585624q^{94} + 13730236994039q^{95} + 17496979214670q^{96} + 10134565481560q^{97} + 70916776240976q^{98} + 2095986297888q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −57.5851 −0.636232 −0.318116 0.948052i \(-0.603050\pi\)
−0.318116 + 0.948052i \(0.603050\pi\)
\(3\) −729.000 −0.577350
\(4\) −4875.95 −0.595209
\(5\) 31633.2 0.905395 0.452698 0.891664i \(-0.350462\pi\)
0.452698 + 0.891664i \(0.350462\pi\)
\(6\) 41979.6 0.367329
\(7\) 267144. 0.858238 0.429119 0.903248i \(-0.358824\pi\)
0.429119 + 0.903248i \(0.358824\pi\)
\(8\) 752520. 1.01492
\(9\) 531441. 0.333333
\(10\) −1.82160e6 −0.576041
\(11\) 3.70473e6 0.630528 0.315264 0.949004i \(-0.397907\pi\)
0.315264 + 0.949004i \(0.397907\pi\)
\(12\) 3.55457e6 0.343644
\(13\) 3.03857e7 1.74597 0.872986 0.487745i \(-0.162180\pi\)
0.872986 + 0.487745i \(0.162180\pi\)
\(14\) −1.53835e7 −0.546038
\(15\) −2.30606e7 −0.522730
\(16\) −3.39015e6 −0.0505172
\(17\) 5.25313e6 0.0527837 0.0263919 0.999652i \(-0.491598\pi\)
0.0263919 + 0.999652i \(0.491598\pi\)
\(18\) −3.06031e7 −0.212077
\(19\) −1.93452e8 −0.943354 −0.471677 0.881771i \(-0.656351\pi\)
−0.471677 + 0.881771i \(0.656351\pi\)
\(20\) −1.54242e8 −0.538899
\(21\) −1.94748e8 −0.495504
\(22\) −2.13337e8 −0.401162
\(23\) −1.22257e8 −0.172204 −0.0861020 0.996286i \(-0.527441\pi\)
−0.0861020 + 0.996286i \(0.527441\pi\)
\(24\) −5.48587e8 −0.585966
\(25\) −2.20043e8 −0.180259
\(26\) −1.74976e9 −1.11084
\(27\) −3.87420e8 −0.192450
\(28\) −1.30258e9 −0.510831
\(29\) 8.14387e8 0.254240 0.127120 0.991887i \(-0.459427\pi\)
0.127120 + 0.991887i \(0.459427\pi\)
\(30\) 1.32795e9 0.332578
\(31\) 1.38541e9 0.280368 0.140184 0.990125i \(-0.455231\pi\)
0.140184 + 0.990125i \(0.455231\pi\)
\(32\) −5.96942e9 −0.982782
\(33\) −2.70075e9 −0.364035
\(34\) −3.02502e8 −0.0335827
\(35\) 8.45061e9 0.777045
\(36\) −2.59128e9 −0.198403
\(37\) −2.86691e10 −1.83697 −0.918487 0.395452i \(-0.870588\pi\)
−0.918487 + 0.395452i \(0.870588\pi\)
\(38\) 1.11400e10 0.600192
\(39\) −2.21512e10 −1.00804
\(40\) 2.38046e10 0.918906
\(41\) −1.17360e10 −0.385855 −0.192927 0.981213i \(-0.561798\pi\)
−0.192927 + 0.981213i \(0.561798\pi\)
\(42\) 1.12146e10 0.315255
\(43\) −2.19728e10 −0.530078 −0.265039 0.964238i \(-0.585385\pi\)
−0.265039 + 0.964238i \(0.585385\pi\)
\(44\) −1.80641e10 −0.375296
\(45\) 1.68112e10 0.301798
\(46\) 7.04019e9 0.109562
\(47\) −4.74856e10 −0.642578 −0.321289 0.946981i \(-0.604116\pi\)
−0.321289 + 0.946981i \(0.604116\pi\)
\(48\) 2.47142e9 0.0291661
\(49\) −2.55232e10 −0.263428
\(50\) 1.26712e10 0.114687
\(51\) −3.82953e9 −0.0304747
\(52\) −1.48159e11 −1.03922
\(53\) −1.45553e11 −0.902042 −0.451021 0.892513i \(-0.648940\pi\)
−0.451021 + 0.892513i \(0.648940\pi\)
\(54\) 2.23097e10 0.122443
\(55\) 1.17193e11 0.570877
\(56\) 2.01031e11 0.871045
\(57\) 1.41026e11 0.544645
\(58\) −4.68966e10 −0.161755
\(59\) −4.21805e10 −0.130189
\(60\) 1.12442e11 0.311134
\(61\) −5.68197e10 −0.141207 −0.0706033 0.997504i \(-0.522492\pi\)
−0.0706033 + 0.997504i \(0.522492\pi\)
\(62\) −7.97793e10 −0.178379
\(63\) 1.41971e11 0.286079
\(64\) 3.71522e11 0.675794
\(65\) 9.61197e11 1.58080
\(66\) 1.55523e11 0.231611
\(67\) 6.47814e11 0.874912 0.437456 0.899240i \(-0.355880\pi\)
0.437456 + 0.899240i \(0.355880\pi\)
\(68\) −2.56140e10 −0.0314173
\(69\) 8.91254e10 0.0994220
\(70\) −4.86630e11 −0.494381
\(71\) −1.68243e11 −0.155868 −0.0779340 0.996959i \(-0.524832\pi\)
−0.0779340 + 0.996959i \(0.524832\pi\)
\(72\) 3.99920e11 0.338308
\(73\) −6.75444e11 −0.522385 −0.261193 0.965287i \(-0.584116\pi\)
−0.261193 + 0.965287i \(0.584116\pi\)
\(74\) 1.65091e12 1.16874
\(75\) 1.60411e11 0.104073
\(76\) 9.43262e11 0.561493
\(77\) 9.89696e11 0.541143
\(78\) 1.27558e12 0.641346
\(79\) −1.56297e11 −0.0723393 −0.0361696 0.999346i \(-0.511516\pi\)
−0.0361696 + 0.999346i \(0.511516\pi\)
\(80\) −1.07241e11 −0.0457380
\(81\) 2.82430e11 0.111111
\(82\) 6.75817e11 0.245493
\(83\) −3.56084e12 −1.19549 −0.597743 0.801687i \(-0.703936\pi\)
−0.597743 + 0.801687i \(0.703936\pi\)
\(84\) 9.49581e11 0.294928
\(85\) 1.66173e11 0.0477901
\(86\) 1.26531e12 0.337253
\(87\) −5.93688e11 −0.146785
\(88\) 2.78788e12 0.639937
\(89\) −6.47668e12 −1.38139 −0.690697 0.723144i \(-0.742696\pi\)
−0.690697 + 0.723144i \(0.742696\pi\)
\(90\) −9.68074e11 −0.192014
\(91\) 8.11735e12 1.49846
\(92\) 5.96120e11 0.102497
\(93\) −1.00997e12 −0.161871
\(94\) 2.73446e12 0.408828
\(95\) −6.11950e12 −0.854108
\(96\) 4.35171e12 0.567410
\(97\) −1.96982e12 −0.240110 −0.120055 0.992767i \(-0.538307\pi\)
−0.120055 + 0.992767i \(0.538307\pi\)
\(98\) 1.46976e12 0.167601
\(99\) 1.96885e12 0.210176
\(100\) 1.07292e12 0.107292
\(101\) −1.43041e13 −1.34082 −0.670411 0.741990i \(-0.733882\pi\)
−0.670411 + 0.741990i \(0.733882\pi\)
\(102\) 2.20524e11 0.0193890
\(103\) −2.57948e12 −0.212858 −0.106429 0.994320i \(-0.533942\pi\)
−0.106429 + 0.994320i \(0.533942\pi\)
\(104\) 2.28658e13 1.77203
\(105\) −6.16050e12 −0.448627
\(106\) 8.38167e12 0.573908
\(107\) 5.39263e12 0.347381 0.173690 0.984800i \(-0.444431\pi\)
0.173690 + 0.984800i \(0.444431\pi\)
\(108\) 1.88904e12 0.114548
\(109\) 3.47738e13 1.98600 0.993002 0.118097i \(-0.0376794\pi\)
0.993002 + 0.118097i \(0.0376794\pi\)
\(110\) −6.74855e12 −0.363210
\(111\) 2.08998e13 1.06058
\(112\) −9.05657e11 −0.0433557
\(113\) 7.73249e12 0.349389 0.174695 0.984623i \(-0.444106\pi\)
0.174695 + 0.984623i \(0.444106\pi\)
\(114\) −8.12102e12 −0.346521
\(115\) −3.86738e12 −0.155913
\(116\) −3.97091e12 −0.151326
\(117\) 1.61482e13 0.581991
\(118\) 2.42897e12 0.0828303
\(119\) 1.40334e12 0.0453010
\(120\) −1.73536e13 −0.530531
\(121\) −2.07977e13 −0.602435
\(122\) 3.27197e12 0.0898402
\(123\) 8.55552e12 0.222773
\(124\) −6.75522e12 −0.166878
\(125\) −4.55754e13 −1.06860
\(126\) −8.17543e12 −0.182013
\(127\) 2.67212e13 0.565109 0.282555 0.959251i \(-0.408818\pi\)
0.282555 + 0.959251i \(0.408818\pi\)
\(128\) 2.75073e13 0.552820
\(129\) 1.60182e13 0.306041
\(130\) −5.53507e13 −1.00575
\(131\) −3.15424e13 −0.545294 −0.272647 0.962114i \(-0.587899\pi\)
−0.272647 + 0.962114i \(0.587899\pi\)
\(132\) 1.31687e13 0.216677
\(133\) −5.16795e13 −0.809622
\(134\) −3.73045e13 −0.556647
\(135\) −1.22554e13 −0.174243
\(136\) 3.95308e12 0.0535714
\(137\) −8.10965e13 −1.04790 −0.523948 0.851750i \(-0.675541\pi\)
−0.523948 + 0.851750i \(0.675541\pi\)
\(138\) −5.13230e12 −0.0632554
\(139\) −1.15642e14 −1.35994 −0.679971 0.733239i \(-0.738008\pi\)
−0.679971 + 0.733239i \(0.738008\pi\)
\(140\) −4.12048e13 −0.462504
\(141\) 3.46170e13 0.370992
\(142\) 9.68828e12 0.0991682
\(143\) 1.12571e14 1.10088
\(144\) −1.80166e12 −0.0168391
\(145\) 2.57617e13 0.230188
\(146\) 3.88956e13 0.332358
\(147\) 1.86064e13 0.152090
\(148\) 1.39789e14 1.09338
\(149\) 2.57327e14 1.92653 0.963264 0.268557i \(-0.0865467\pi\)
0.963264 + 0.268557i \(0.0865467\pi\)
\(150\) −9.23731e12 −0.0662144
\(151\) −2.08141e13 −0.142892 −0.0714458 0.997444i \(-0.522761\pi\)
−0.0714458 + 0.997444i \(0.522761\pi\)
\(152\) −1.45576e14 −0.957431
\(153\) 2.79173e12 0.0175946
\(154\) −5.69918e13 −0.344292
\(155\) 4.38251e13 0.253844
\(156\) 1.08008e14 0.599993
\(157\) −1.21070e14 −0.645191 −0.322595 0.946537i \(-0.604555\pi\)
−0.322595 + 0.946537i \(0.604555\pi\)
\(158\) 9.00037e12 0.0460245
\(159\) 1.06108e14 0.520794
\(160\) −1.88832e14 −0.889806
\(161\) −3.26602e13 −0.147792
\(162\) −1.62637e13 −0.0706924
\(163\) −9.75359e13 −0.407329 −0.203664 0.979041i \(-0.565285\pi\)
−0.203664 + 0.979041i \(0.565285\pi\)
\(164\) 5.72240e13 0.229664
\(165\) −8.54334e13 −0.329596
\(166\) 2.05051e14 0.760607
\(167\) −3.90228e13 −0.139207 −0.0696036 0.997575i \(-0.522173\pi\)
−0.0696036 + 0.997575i \(0.522173\pi\)
\(168\) −1.46552e14 −0.502898
\(169\) 6.20415e14 2.04842
\(170\) −9.56911e12 −0.0304056
\(171\) −1.02808e14 −0.314451
\(172\) 1.07138e14 0.315507
\(173\) −3.31154e14 −0.939141 −0.469570 0.882895i \(-0.655591\pi\)
−0.469570 + 0.882895i \(0.655591\pi\)
\(174\) 3.41876e13 0.0933896
\(175\) −5.87831e13 −0.154705
\(176\) −1.25596e13 −0.0318525
\(177\) 3.07496e13 0.0751646
\(178\) 3.72961e14 0.878887
\(179\) 1.86211e14 0.423116 0.211558 0.977365i \(-0.432146\pi\)
0.211558 + 0.977365i \(0.432146\pi\)
\(180\) −8.19705e13 −0.179633
\(181\) −7.41190e13 −0.156682 −0.0783409 0.996927i \(-0.524962\pi\)
−0.0783409 + 0.996927i \(0.524962\pi\)
\(182\) −4.67438e14 −0.953368
\(183\) 4.14216e13 0.0815257
\(184\) −9.20009e13 −0.174774
\(185\) −9.06896e14 −1.66319
\(186\) 5.81591e13 0.102987
\(187\) 1.94614e13 0.0332816
\(188\) 2.31537e14 0.382468
\(189\) −1.03497e14 −0.165168
\(190\) 3.52392e14 0.543411
\(191\) −1.00935e15 −1.50426 −0.752130 0.659015i \(-0.770973\pi\)
−0.752130 + 0.659015i \(0.770973\pi\)
\(192\) −2.70839e14 −0.390170
\(193\) 1.02739e15 1.43091 0.715456 0.698658i \(-0.246219\pi\)
0.715456 + 0.698658i \(0.246219\pi\)
\(194\) 1.13432e14 0.152765
\(195\) −7.00713e14 −0.912672
\(196\) 1.24450e14 0.156795
\(197\) −3.08783e14 −0.376376 −0.188188 0.982133i \(-0.560261\pi\)
−0.188188 + 0.982133i \(0.560261\pi\)
\(198\) −1.13376e14 −0.133721
\(199\) −2.31325e14 −0.264045 −0.132023 0.991247i \(-0.542147\pi\)
−0.132023 + 0.991247i \(0.542147\pi\)
\(200\) −1.65587e14 −0.182949
\(201\) −4.72257e14 −0.505130
\(202\) 8.23702e14 0.853073
\(203\) 2.17558e14 0.218198
\(204\) 1.86726e13 0.0181388
\(205\) −3.71246e14 −0.349351
\(206\) 1.48540e14 0.135427
\(207\) −6.49724e13 −0.0574013
\(208\) −1.03012e14 −0.0882016
\(209\) −7.16687e14 −0.594811
\(210\) 3.54753e14 0.285431
\(211\) −1.97669e15 −1.54206 −0.771031 0.636798i \(-0.780259\pi\)
−0.771031 + 0.636798i \(0.780259\pi\)
\(212\) 7.09708e14 0.536904
\(213\) 1.22649e14 0.0899905
\(214\) −3.10535e14 −0.221015
\(215\) −6.95069e14 −0.479930
\(216\) −2.91542e14 −0.195322
\(217\) 3.70105e14 0.240623
\(218\) −2.00245e15 −1.26356
\(219\) 4.92399e14 0.301599
\(220\) −5.71425e14 −0.339791
\(221\) 1.59620e14 0.0921589
\(222\) −1.20352e15 −0.674773
\(223\) −1.00091e15 −0.545023 −0.272511 0.962153i \(-0.587854\pi\)
−0.272511 + 0.962153i \(0.587854\pi\)
\(224\) −1.59469e15 −0.843461
\(225\) −1.16940e14 −0.0600864
\(226\) −4.45277e14 −0.222293
\(227\) −3.14480e15 −1.52555 −0.762773 0.646667i \(-0.776163\pi\)
−0.762773 + 0.646667i \(0.776163\pi\)
\(228\) −6.87638e14 −0.324178
\(229\) −1.80493e15 −0.827044 −0.413522 0.910494i \(-0.635702\pi\)
−0.413522 + 0.910494i \(0.635702\pi\)
\(230\) 2.22704e14 0.0991966
\(231\) −7.21488e14 −0.312429
\(232\) 6.12842e14 0.258034
\(233\) 1.72121e15 0.704727 0.352363 0.935863i \(-0.385378\pi\)
0.352363 + 0.935863i \(0.385378\pi\)
\(234\) −9.29896e14 −0.370281
\(235\) −1.50212e15 −0.581787
\(236\) 2.05670e14 0.0774896
\(237\) 1.13940e14 0.0417651
\(238\) −8.08115e13 −0.0288219
\(239\) −3.39273e15 −1.17751 −0.588753 0.808313i \(-0.700381\pi\)
−0.588753 + 0.808313i \(0.700381\pi\)
\(240\) 7.81789e13 0.0264068
\(241\) 2.85588e15 0.938920 0.469460 0.882954i \(-0.344449\pi\)
0.469460 + 0.882954i \(0.344449\pi\)
\(242\) 1.19764e15 0.383288
\(243\) −2.05891e14 −0.0641500
\(244\) 2.77050e14 0.0840475
\(245\) −8.07382e14 −0.238506
\(246\) −4.92671e14 −0.141735
\(247\) −5.87817e15 −1.64707
\(248\) 1.04255e15 0.284552
\(249\) 2.59585e15 0.690215
\(250\) 2.62447e15 0.679878
\(251\) 6.96415e15 1.75788 0.878939 0.476934i \(-0.158252\pi\)
0.878939 + 0.476934i \(0.158252\pi\)
\(252\) −6.92244e14 −0.170277
\(253\) −4.52930e14 −0.108579
\(254\) −1.53875e15 −0.359540
\(255\) −1.21140e14 −0.0275916
\(256\) −4.62752e15 −1.02752
\(257\) −8.23785e14 −0.178340 −0.0891700 0.996016i \(-0.528421\pi\)
−0.0891700 + 0.996016i \(0.528421\pi\)
\(258\) −9.22408e14 −0.194713
\(259\) −7.65877e15 −1.57656
\(260\) −4.68675e15 −0.940904
\(261\) 4.32798e14 0.0847466
\(262\) 1.81637e15 0.346934
\(263\) −6.43801e14 −0.119961 −0.0599804 0.998200i \(-0.519104\pi\)
−0.0599804 + 0.998200i \(0.519104\pi\)
\(264\) −2.03237e15 −0.369468
\(265\) −4.60430e15 −0.816705
\(266\) 2.97597e15 0.515107
\(267\) 4.72150e15 0.797548
\(268\) −3.15871e15 −0.520755
\(269\) 3.19797e15 0.514617 0.257308 0.966329i \(-0.417164\pi\)
0.257308 + 0.966329i \(0.417164\pi\)
\(270\) 7.05726e14 0.110859
\(271\) −4.06076e15 −0.622740 −0.311370 0.950289i \(-0.600788\pi\)
−0.311370 + 0.950289i \(0.600788\pi\)
\(272\) −1.78089e13 −0.00266648
\(273\) −5.91755e15 −0.865136
\(274\) 4.66995e15 0.666705
\(275\) −8.15201e14 −0.113659
\(276\) −4.34571e14 −0.0591769
\(277\) −1.06729e16 −1.41960 −0.709798 0.704405i \(-0.751214\pi\)
−0.709798 + 0.704405i \(0.751214\pi\)
\(278\) 6.65927e15 0.865238
\(279\) 7.36266e14 0.0934561
\(280\) 6.35925e15 0.788640
\(281\) 2.65538e15 0.321762 0.160881 0.986974i \(-0.448566\pi\)
0.160881 + 0.986974i \(0.448566\pi\)
\(282\) −1.99342e15 −0.236037
\(283\) −2.80805e15 −0.324932 −0.162466 0.986714i \(-0.551945\pi\)
−0.162466 + 0.986714i \(0.551945\pi\)
\(284\) 8.20344e14 0.0927741
\(285\) 4.46112e15 0.493119
\(286\) −6.48241e15 −0.700418
\(287\) −3.13519e15 −0.331155
\(288\) −3.17239e15 −0.327594
\(289\) −9.87698e15 −0.997214
\(290\) −1.48349e15 −0.146453
\(291\) 1.43600e15 0.138627
\(292\) 3.29343e15 0.310929
\(293\) 1.12425e16 1.03806 0.519032 0.854755i \(-0.326293\pi\)
0.519032 + 0.854755i \(0.326293\pi\)
\(294\) −1.07145e15 −0.0967645
\(295\) −1.33431e15 −0.117872
\(296\) −2.15741e16 −1.86439
\(297\) −1.43529e15 −0.121345
\(298\) −1.48182e16 −1.22572
\(299\) −3.71487e15 −0.300663
\(300\) −7.82159e14 −0.0619451
\(301\) −5.86989e15 −0.454933
\(302\) 1.19858e15 0.0909122
\(303\) 1.04277e16 0.774123
\(304\) 6.55831e14 0.0476555
\(305\) −1.79739e15 −0.127848
\(306\) −1.60762e14 −0.0111942
\(307\) 2.19317e16 1.49511 0.747555 0.664200i \(-0.231228\pi\)
0.747555 + 0.664200i \(0.231228\pi\)
\(308\) −4.82571e15 −0.322093
\(309\) 1.88044e15 0.122894
\(310\) −2.52368e15 −0.161504
\(311\) −2.42365e16 −1.51889 −0.759446 0.650570i \(-0.774530\pi\)
−0.759446 + 0.650570i \(0.774530\pi\)
\(312\) −1.66692e16 −1.02308
\(313\) 1.66454e16 1.00059 0.500295 0.865855i \(-0.333225\pi\)
0.500295 + 0.865855i \(0.333225\pi\)
\(314\) 6.97182e15 0.410491
\(315\) 4.49100e15 0.259015
\(316\) 7.62096e14 0.0430570
\(317\) 2.78403e16 1.54095 0.770474 0.637471i \(-0.220019\pi\)
0.770474 + 0.637471i \(0.220019\pi\)
\(318\) −6.11024e15 −0.331346
\(319\) 3.01708e15 0.160305
\(320\) 1.17524e16 0.611861
\(321\) −3.93123e15 −0.200560
\(322\) 1.88074e15 0.0940300
\(323\) −1.01623e15 −0.0497937
\(324\) −1.37711e15 −0.0661343
\(325\) −6.68616e15 −0.314728
\(326\) 5.61662e15 0.259156
\(327\) −2.53501e16 −1.14662
\(328\) −8.83154e15 −0.391613
\(329\) −1.26855e16 −0.551485
\(330\) 4.91969e15 0.209699
\(331\) −3.38160e16 −1.41332 −0.706661 0.707553i \(-0.749799\pi\)
−0.706661 + 0.707553i \(0.749799\pi\)
\(332\) 1.73625e16 0.711565
\(333\) −1.52359e16 −0.612325
\(334\) 2.24713e15 0.0885680
\(335\) 2.04924e16 0.792141
\(336\) 6.60224e14 0.0250314
\(337\) −9.87424e15 −0.367206 −0.183603 0.983001i \(-0.558776\pi\)
−0.183603 + 0.983001i \(0.558776\pi\)
\(338\) −3.57267e16 −1.30327
\(339\) −5.63699e15 −0.201720
\(340\) −8.10253e14 −0.0284451
\(341\) 5.13259e15 0.176780
\(342\) 5.92023e15 0.200064
\(343\) −3.27017e16 −1.08432
\(344\) −1.65349e16 −0.537988
\(345\) 2.81932e15 0.0900162
\(346\) 1.90696e16 0.597511
\(347\) 4.99385e16 1.53566 0.767828 0.640656i \(-0.221337\pi\)
0.767828 + 0.640656i \(0.221337\pi\)
\(348\) 2.89479e15 0.0873680
\(349\) −1.42517e16 −0.422183 −0.211091 0.977466i \(-0.567702\pi\)
−0.211091 + 0.977466i \(0.567702\pi\)
\(350\) 3.38503e15 0.0984285
\(351\) −1.17720e16 −0.336013
\(352\) −2.21151e16 −0.619672
\(353\) 3.05197e16 0.839547 0.419773 0.907629i \(-0.362110\pi\)
0.419773 + 0.907629i \(0.362110\pi\)
\(354\) −1.77072e15 −0.0478221
\(355\) −5.32206e15 −0.141122
\(356\) 3.15800e16 0.822218
\(357\) −1.02303e15 −0.0261545
\(358\) −1.07230e16 −0.269200
\(359\) 2.10998e16 0.520192 0.260096 0.965583i \(-0.416246\pi\)
0.260096 + 0.965583i \(0.416246\pi\)
\(360\) 1.26507e16 0.306302
\(361\) −4.62936e15 −0.110084
\(362\) 4.26815e15 0.0996860
\(363\) 1.51615e16 0.347816
\(364\) −3.95798e16 −0.891897
\(365\) −2.13665e16 −0.472965
\(366\) −2.38527e15 −0.0518692
\(367\) −2.42514e16 −0.518092 −0.259046 0.965865i \(-0.583408\pi\)
−0.259046 + 0.965865i \(0.583408\pi\)
\(368\) 4.14470e14 0.00869926
\(369\) −6.23697e15 −0.128618
\(370\) 5.22237e16 1.05817
\(371\) −3.88835e16 −0.774167
\(372\) 4.92455e15 0.0963469
\(373\) 1.03626e17 1.99232 0.996161 0.0875416i \(-0.0279011\pi\)
0.996161 + 0.0875416i \(0.0279011\pi\)
\(374\) −1.12069e15 −0.0211748
\(375\) 3.32245e16 0.616957
\(376\) −3.57338e16 −0.652167
\(377\) 2.47457e16 0.443896
\(378\) 5.95989e15 0.105085
\(379\) 1.68371e16 0.291818 0.145909 0.989298i \(-0.453389\pi\)
0.145909 + 0.989298i \(0.453389\pi\)
\(380\) 2.98384e16 0.508373
\(381\) −1.94798e16 −0.326266
\(382\) 5.81233e16 0.957058
\(383\) 8.78160e16 1.42161 0.710807 0.703387i \(-0.248330\pi\)
0.710807 + 0.703387i \(0.248330\pi\)
\(384\) −2.00529e16 −0.319171
\(385\) 3.13073e16 0.489948
\(386\) −5.91624e16 −0.910391
\(387\) −1.16772e16 −0.176693
\(388\) 9.60474e15 0.142915
\(389\) 3.56286e15 0.0521347 0.0260673 0.999660i \(-0.491702\pi\)
0.0260673 + 0.999660i \(0.491702\pi\)
\(390\) 4.03506e16 0.580671
\(391\) −6.42232e14 −0.00908956
\(392\) −1.92067e16 −0.267359
\(393\) 2.29944e16 0.314826
\(394\) 1.77813e16 0.239463
\(395\) −4.94417e15 −0.0654956
\(396\) −9.60000e15 −0.125099
\(397\) −8.74066e15 −0.112048 −0.0560242 0.998429i \(-0.517842\pi\)
−0.0560242 + 0.998429i \(0.517842\pi\)
\(398\) 1.33209e16 0.167994
\(399\) 3.76743e16 0.467435
\(400\) 7.45979e14 0.00910619
\(401\) 9.14289e16 1.09811 0.549054 0.835787i \(-0.314988\pi\)
0.549054 + 0.835787i \(0.314988\pi\)
\(402\) 2.71950e16 0.321380
\(403\) 4.20968e16 0.489515
\(404\) 6.97460e16 0.798069
\(405\) 8.93415e15 0.100599
\(406\) −1.25281e16 −0.138825
\(407\) −1.06211e17 −1.15826
\(408\) −2.88180e15 −0.0309295
\(409\) 3.81780e15 0.0403284 0.0201642 0.999797i \(-0.493581\pi\)
0.0201642 + 0.999797i \(0.493581\pi\)
\(410\) 2.13783e16 0.222268
\(411\) 5.91193e16 0.605003
\(412\) 1.25774e16 0.126695
\(413\) −1.12683e16 −0.111733
\(414\) 3.74145e15 0.0365205
\(415\) −1.12641e17 −1.08239
\(416\) −1.81385e17 −1.71591
\(417\) 8.43032e16 0.785163
\(418\) 4.12705e16 0.378438
\(419\) 5.77997e16 0.521837 0.260918 0.965361i \(-0.415975\pi\)
0.260918 + 0.965361i \(0.415975\pi\)
\(420\) 3.00383e16 0.267027
\(421\) −3.64550e15 −0.0319097 −0.0159549 0.999873i \(-0.505079\pi\)
−0.0159549 + 0.999873i \(0.505079\pi\)
\(422\) 1.13828e17 0.981109
\(423\) −2.52358e16 −0.214193
\(424\) −1.09531e17 −0.915503
\(425\) −1.15591e15 −0.00951475
\(426\) −7.06276e15 −0.0572548
\(427\) −1.51790e16 −0.121189
\(428\) −2.62942e16 −0.206764
\(429\) −8.20641e16 −0.635596
\(430\) 4.00257e16 0.305347
\(431\) −8.89222e16 −0.668202 −0.334101 0.942537i \(-0.608433\pi\)
−0.334101 + 0.942537i \(0.608433\pi\)
\(432\) 1.31341e15 0.00972203
\(433\) −3.07518e15 −0.0224233 −0.0112116 0.999937i \(-0.503569\pi\)
−0.0112116 + 0.999937i \(0.503569\pi\)
\(434\) −2.13125e16 −0.153092
\(435\) −1.87803e16 −0.132899
\(436\) −1.69555e17 −1.18209
\(437\) 2.36509e16 0.162449
\(438\) −2.83549e16 −0.191887
\(439\) 5.16973e16 0.344706 0.172353 0.985035i \(-0.444863\pi\)
0.172353 + 0.985035i \(0.444863\pi\)
\(440\) 8.81897e16 0.579396
\(441\) −1.35641e16 −0.0878092
\(442\) −9.19173e15 −0.0586344
\(443\) −3.39507e16 −0.213415 −0.106707 0.994290i \(-0.534031\pi\)
−0.106707 + 0.994290i \(0.534031\pi\)
\(444\) −1.01906e17 −0.631265
\(445\) −2.04878e17 −1.25071
\(446\) 5.76377e16 0.346761
\(447\) −1.87592e17 −1.11228
\(448\) 9.92497e16 0.579992
\(449\) 4.80872e16 0.276967 0.138484 0.990365i \(-0.455777\pi\)
0.138484 + 0.990365i \(0.455777\pi\)
\(450\) 6.73400e15 0.0382289
\(451\) −4.34786e16 −0.243292
\(452\) −3.77033e16 −0.207960
\(453\) 1.51734e16 0.0824985
\(454\) 1.81094e17 0.970601
\(455\) 2.56778e17 1.35670
\(456\) 1.06125e17 0.552773
\(457\) 3.55915e17 1.82764 0.913821 0.406117i \(-0.133117\pi\)
0.913821 + 0.406117i \(0.133117\pi\)
\(458\) 1.03937e17 0.526192
\(459\) −2.03517e15 −0.0101582
\(460\) 1.88572e16 0.0928006
\(461\) −3.24418e17 −1.57416 −0.787081 0.616850i \(-0.788409\pi\)
−0.787081 + 0.616850i \(0.788409\pi\)
\(462\) 4.15470e16 0.198777
\(463\) 1.39573e17 0.658451 0.329226 0.944251i \(-0.393212\pi\)
0.329226 + 0.944251i \(0.393212\pi\)
\(464\) −2.76089e15 −0.0128435
\(465\) −3.19485e16 −0.146557
\(466\) −9.91162e16 −0.448370
\(467\) −6.92696e16 −0.309017 −0.154509 0.987991i \(-0.549379\pi\)
−0.154509 + 0.987991i \(0.549379\pi\)
\(468\) −7.87379e16 −0.346406
\(469\) 1.73059e17 0.750882
\(470\) 8.64998e16 0.370151
\(471\) 8.82599e16 0.372501
\(472\) −3.17417e16 −0.132132
\(473\) −8.14032e16 −0.334229
\(474\) −6.56127e15 −0.0265723
\(475\) 4.25678e16 0.170048
\(476\) −6.84262e15 −0.0269635
\(477\) −7.73526e16 −0.300681
\(478\) 1.95371e17 0.749167
\(479\) 1.85239e17 0.700730 0.350365 0.936613i \(-0.386058\pi\)
0.350365 + 0.936613i \(0.386058\pi\)
\(480\) 1.37658e17 0.513730
\(481\) −8.71131e17 −3.20730
\(482\) −1.64456e17 −0.597371
\(483\) 2.38093e16 0.0853277
\(484\) 1.01408e17 0.358575
\(485\) −6.23117e16 −0.217394
\(486\) 1.18563e16 0.0408143
\(487\) 2.70563e17 0.919030 0.459515 0.888170i \(-0.348023\pi\)
0.459515 + 0.888170i \(0.348023\pi\)
\(488\) −4.27580e16 −0.143314
\(489\) 7.11037e16 0.235171
\(490\) 4.64932e16 0.151745
\(491\) 5.77957e17 1.86151 0.930755 0.365642i \(-0.119151\pi\)
0.930755 + 0.365642i \(0.119151\pi\)
\(492\) −4.17163e16 −0.132597
\(493\) 4.27808e15 0.0134197
\(494\) 3.38495e17 1.04792
\(495\) 6.22809e16 0.190292
\(496\) −4.69676e15 −0.0141634
\(497\) −4.49450e16 −0.133772
\(498\) −1.49483e17 −0.439137
\(499\) −1.12887e17 −0.327333 −0.163667 0.986516i \(-0.552332\pi\)
−0.163667 + 0.986516i \(0.552332\pi\)
\(500\) 2.22224e17 0.636041
\(501\) 2.84476e16 0.0803713
\(502\) −4.01031e17 −1.11842
\(503\) 5.92794e17 1.63197 0.815985 0.578073i \(-0.196195\pi\)
0.815985 + 0.578073i \(0.196195\pi\)
\(504\) 1.06836e17 0.290348
\(505\) −4.52484e17 −1.21397
\(506\) 2.60820e16 0.0690817
\(507\) −4.52283e17 −1.18266
\(508\) −1.30291e17 −0.336358
\(509\) 1.88535e17 0.480537 0.240269 0.970706i \(-0.422765\pi\)
0.240269 + 0.970706i \(0.422765\pi\)
\(510\) 6.97588e15 0.0175547
\(511\) −1.80441e17 −0.448331
\(512\) 4.11363e16 0.100918
\(513\) 7.49472e16 0.181548
\(514\) 4.74378e16 0.113466
\(515\) −8.15972e16 −0.192721
\(516\) −7.81038e16 −0.182158
\(517\) −1.75921e17 −0.405163
\(518\) 4.41031e17 1.00306
\(519\) 2.41412e17 0.542213
\(520\) 7.23320e17 1.60438
\(521\) 2.58570e17 0.566412 0.283206 0.959059i \(-0.408602\pi\)
0.283206 + 0.959059i \(0.408602\pi\)
\(522\) −2.49228e16 −0.0539185
\(523\) −2.33350e17 −0.498594 −0.249297 0.968427i \(-0.580199\pi\)
−0.249297 + 0.968427i \(0.580199\pi\)
\(524\) 1.53799e17 0.324564
\(525\) 4.28529e16 0.0893192
\(526\) 3.70734e16 0.0763228
\(527\) 7.27776e15 0.0147989
\(528\) 9.15594e15 0.0183900
\(529\) −4.89090e17 −0.970346
\(530\) 2.65139e17 0.519614
\(531\) −2.24165e16 −0.0433963
\(532\) 2.51987e17 0.481894
\(533\) −3.56605e17 −0.673691
\(534\) −2.71888e17 −0.507426
\(535\) 1.70586e17 0.314517
\(536\) 4.87493e17 0.887968
\(537\) −1.35748e17 −0.244286
\(538\) −1.84155e17 −0.327416
\(539\) −9.45568e16 −0.166099
\(540\) 5.97565e16 0.103711
\(541\) 1.90903e17 0.327364 0.163682 0.986513i \(-0.447663\pi\)
0.163682 + 0.986513i \(0.447663\pi\)
\(542\) 2.33839e17 0.396207
\(543\) 5.40327e16 0.0904603
\(544\) −3.13581e16 −0.0518749
\(545\) 1.10001e18 1.79812
\(546\) 3.40763e17 0.550427
\(547\) 9.96223e17 1.59015 0.795076 0.606509i \(-0.207431\pi\)
0.795076 + 0.606509i \(0.207431\pi\)
\(548\) 3.95423e17 0.623717
\(549\) −3.01963e16 −0.0470689
\(550\) 4.69434e16 0.0723132
\(551\) −1.57545e17 −0.239838
\(552\) 6.70686e16 0.100906
\(553\) −4.17537e16 −0.0620843
\(554\) 6.14602e17 0.903192
\(555\) 6.61127e17 0.960242
\(556\) 5.63866e17 0.809450
\(557\) −3.59072e17 −0.509474 −0.254737 0.967010i \(-0.581989\pi\)
−0.254737 + 0.967010i \(0.581989\pi\)
\(558\) −4.23980e16 −0.0594597
\(559\) −6.67658e17 −0.925502
\(560\) −2.86488e16 −0.0392541
\(561\) −1.41874e16 −0.0192151
\(562\) −1.52910e17 −0.204715
\(563\) −5.87386e17 −0.777354 −0.388677 0.921374i \(-0.627068\pi\)
−0.388677 + 0.921374i \(0.627068\pi\)
\(564\) −1.68791e17 −0.220818
\(565\) 2.44604e17 0.316336
\(566\) 1.61702e17 0.206732
\(567\) 7.54493e16 0.0953598
\(568\) −1.26606e17 −0.158194
\(569\) 7.28452e17 0.899852 0.449926 0.893066i \(-0.351450\pi\)
0.449926 + 0.893066i \(0.351450\pi\)
\(570\) −2.56894e17 −0.313738
\(571\) 5.87647e17 0.709548 0.354774 0.934952i \(-0.384558\pi\)
0.354774 + 0.934952i \(0.384558\pi\)
\(572\) −5.48890e17 −0.655256
\(573\) 7.35813e17 0.868485
\(574\) 1.80540e17 0.210691
\(575\) 2.69018e16 0.0310414
\(576\) 1.97442e17 0.225265
\(577\) −1.49386e17 −0.168526 −0.0842632 0.996444i \(-0.526854\pi\)
−0.0842632 + 0.996444i \(0.526854\pi\)
\(578\) 5.68767e17 0.634459
\(579\) −7.48967e17 −0.826137
\(580\) −1.25613e17 −0.137010
\(581\) −9.51256e17 −1.02601
\(582\) −8.26921e16 −0.0881992
\(583\) −5.39233e17 −0.568763
\(584\) −5.08285e17 −0.530181
\(585\) 5.10819e17 0.526932
\(586\) −6.47402e17 −0.660449
\(587\) −7.84995e17 −0.791989 −0.395994 0.918253i \(-0.629600\pi\)
−0.395994 + 0.918253i \(0.629600\pi\)
\(588\) −9.07242e16 −0.0905254
\(589\) −2.68011e17 −0.264486
\(590\) 7.68362e16 0.0749942
\(591\) 2.25103e17 0.217301
\(592\) 9.71925e16 0.0927987
\(593\) −6.68703e17 −0.631506 −0.315753 0.948841i \(-0.602257\pi\)
−0.315753 + 0.948841i \(0.602257\pi\)
\(594\) 8.26513e16 0.0772036
\(595\) 4.43921e16 0.0410153
\(596\) −1.25472e18 −1.14669
\(597\) 1.68636e17 0.152446
\(598\) 2.13921e17 0.191292
\(599\) −9.64228e17 −0.852914 −0.426457 0.904508i \(-0.640238\pi\)
−0.426457 + 0.904508i \(0.640238\pi\)
\(600\) 1.20713e17 0.105626
\(601\) −1.13508e18 −0.982523 −0.491261 0.871012i \(-0.663464\pi\)
−0.491261 + 0.871012i \(0.663464\pi\)
\(602\) 3.38018e17 0.289443
\(603\) 3.44275e17 0.291637
\(604\) 1.01488e17 0.0850503
\(605\) −6.57897e17 −0.545441
\(606\) −6.00479e17 −0.492522
\(607\) −1.14450e18 −0.928733 −0.464367 0.885643i \(-0.653718\pi\)
−0.464367 + 0.885643i \(0.653718\pi\)
\(608\) 1.15480e18 0.927111
\(609\) −1.58600e17 −0.125977
\(610\) 1.03503e17 0.0813409
\(611\) −1.44288e18 −1.12192
\(612\) −1.36123e16 −0.0104724
\(613\) 2.91443e17 0.221851 0.110925 0.993829i \(-0.464619\pi\)
0.110925 + 0.993829i \(0.464619\pi\)
\(614\) −1.26294e18 −0.951236
\(615\) 2.70638e17 0.201698
\(616\) 7.44766e17 0.549218
\(617\) −4.37683e17 −0.319379 −0.159689 0.987167i \(-0.551049\pi\)
−0.159689 + 0.987167i \(0.551049\pi\)
\(618\) −1.08285e17 −0.0781888
\(619\) −5.87911e17 −0.420071 −0.210036 0.977694i \(-0.567358\pi\)
−0.210036 + 0.977694i \(0.567358\pi\)
\(620\) −2.13689e17 −0.151090
\(621\) 4.73649e16 0.0331407
\(622\) 1.39566e18 0.966368
\(623\) −1.73021e18 −1.18556
\(624\) 7.50958e16 0.0509232
\(625\) −1.17309e18 −0.787247
\(626\) −9.58527e17 −0.636607
\(627\) 5.22465e17 0.343414
\(628\) 5.90331e17 0.384024
\(629\) −1.50602e17 −0.0969623
\(630\) −2.58615e17 −0.164794
\(631\) −4.53142e17 −0.285788 −0.142894 0.989738i \(-0.545641\pi\)
−0.142894 + 0.989738i \(0.545641\pi\)
\(632\) −1.17616e17 −0.0734188
\(633\) 1.44100e18 0.890310
\(634\) −1.60319e18 −0.980401
\(635\) 8.45278e17 0.511647
\(636\) −5.17377e17 −0.309982
\(637\) −7.75542e17 −0.459937
\(638\) −1.73739e17 −0.101991
\(639\) −8.94111e16 −0.0519560
\(640\) 8.70146e17 0.500521
\(641\) −1.30602e18 −0.743659 −0.371830 0.928301i \(-0.621269\pi\)
−0.371830 + 0.928301i \(0.621269\pi\)
\(642\) 2.26380e17 0.127603
\(643\) −2.65976e18 −1.48413 −0.742064 0.670329i \(-0.766153\pi\)
−0.742064 + 0.670329i \(0.766153\pi\)
\(644\) 1.59250e17 0.0879671
\(645\) 5.06706e17 0.277088
\(646\) 5.85196e16 0.0316803
\(647\) −1.76549e18 −0.946210 −0.473105 0.881006i \(-0.656867\pi\)
−0.473105 + 0.881006i \(0.656867\pi\)
\(648\) 2.12534e17 0.112769
\(649\) −1.56268e17 −0.0820877
\(650\) 3.85024e17 0.200240
\(651\) −2.69806e17 −0.138924
\(652\) 4.75581e17 0.242446
\(653\) 2.17988e18 1.10026 0.550131 0.835078i \(-0.314578\pi\)
0.550131 + 0.835078i \(0.314578\pi\)
\(654\) 1.45979e18 0.729516
\(655\) −9.97787e17 −0.493707
\(656\) 3.97867e16 0.0194923
\(657\) −3.58959e17 −0.174128
\(658\) 7.30495e17 0.350872
\(659\) 1.21068e18 0.575803 0.287901 0.957660i \(-0.407042\pi\)
0.287901 + 0.957660i \(0.407042\pi\)
\(660\) 4.16569e17 0.196179
\(661\) −3.38669e18 −1.57931 −0.789653 0.613553i \(-0.789740\pi\)
−0.789653 + 0.613553i \(0.789740\pi\)
\(662\) 1.94730e18 0.899200
\(663\) −1.16363e17 −0.0532080
\(664\) −2.67960e18 −1.21333
\(665\) −1.63479e18 −0.733028
\(666\) 8.77363e17 0.389580
\(667\) −9.95645e16 −0.0437811
\(668\) 1.90273e17 0.0828574
\(669\) 7.29666e17 0.314669
\(670\) −1.18006e18 −0.503985
\(671\) −2.10502e17 −0.0890347
\(672\) 1.16253e18 0.486972
\(673\) −4.57591e18 −1.89836 −0.949181 0.314730i \(-0.898086\pi\)
−0.949181 + 0.314730i \(0.898086\pi\)
\(674\) 5.68610e17 0.233628
\(675\) 8.52492e16 0.0346909
\(676\) −3.02511e18 −1.21924
\(677\) −1.36017e18 −0.542960 −0.271480 0.962444i \(-0.587513\pi\)
−0.271480 + 0.962444i \(0.587513\pi\)
\(678\) 3.24607e17 0.128341
\(679\) −5.26224e17 −0.206071
\(680\) 1.25049e17 0.0485033
\(681\) 2.29256e18 0.880774
\(682\) −2.95561e17 −0.112473
\(683\) −2.69603e18 −1.01623 −0.508113 0.861291i \(-0.669657\pi\)
−0.508113 + 0.861291i \(0.669657\pi\)
\(684\) 5.01288e17 0.187164
\(685\) −2.56534e18 −0.948760
\(686\) 1.88313e18 0.689880
\(687\) 1.31579e18 0.477494
\(688\) 7.44910e16 0.0267780
\(689\) −4.42272e18 −1.57494
\(690\) −1.62351e17 −0.0572712
\(691\) 7.32511e17 0.255981 0.127990 0.991775i \(-0.459147\pi\)
0.127990 + 0.991775i \(0.459147\pi\)
\(692\) 1.61469e18 0.558985
\(693\) 5.25965e17 0.180381
\(694\) −2.87572e18 −0.977033
\(695\) −3.65814e18 −1.23128
\(696\) −4.46762e17 −0.148976
\(697\) −6.16505e16 −0.0203668
\(698\) 8.20685e17 0.268606
\(699\) −1.25476e18 −0.406874
\(700\) 2.86624e17 0.0920820
\(701\) 5.35162e17 0.170340 0.0851702 0.996366i \(-0.472857\pi\)
0.0851702 + 0.996366i \(0.472857\pi\)
\(702\) 6.77894e17 0.213782
\(703\) 5.54609e18 1.73292
\(704\) 1.37639e18 0.426107
\(705\) 1.09505e18 0.335895
\(706\) −1.75748e18 −0.534146
\(707\) −3.82124e18 −1.15074
\(708\) −1.49934e17 −0.0447387
\(709\) −1.13858e18 −0.336637 −0.168319 0.985733i \(-0.553834\pi\)
−0.168319 + 0.985733i \(0.553834\pi\)
\(710\) 3.06472e17 0.0897865
\(711\) −8.30626e16 −0.0241131
\(712\) −4.87383e18 −1.40201
\(713\) −1.69377e17 −0.0482805
\(714\) 5.89116e16 0.0166403
\(715\) 3.56098e18 0.996735
\(716\) −9.07954e17 −0.251843
\(717\) 2.47330e18 0.679834
\(718\) −1.21503e18 −0.330963
\(719\) 2.78826e18 0.752653 0.376327 0.926487i \(-0.377187\pi\)
0.376327 + 0.926487i \(0.377187\pi\)
\(720\) −5.69924e16 −0.0152460
\(721\) −6.89091e17 −0.182683
\(722\) 2.66582e17 0.0700389
\(723\) −2.08193e18 −0.542086
\(724\) 3.61401e17 0.0932585
\(725\) −1.79200e17 −0.0458291
\(726\) −8.73077e17 −0.221291
\(727\) −6.34339e18 −1.59348 −0.796742 0.604319i \(-0.793445\pi\)
−0.796742 + 0.604319i \(0.793445\pi\)
\(728\) 6.10846e18 1.52082
\(729\) 1.50095e17 0.0370370
\(730\) 1.23039e18 0.300916
\(731\) −1.15426e17 −0.0279795
\(732\) −2.01970e17 −0.0485248
\(733\) −5.37980e18 −1.28112 −0.640561 0.767907i \(-0.721298\pi\)
−0.640561 + 0.767907i \(0.721298\pi\)
\(734\) 1.39652e18 0.329627
\(735\) 5.88582e17 0.137702
\(736\) 7.29804e17 0.169239
\(737\) 2.39998e18 0.551656
\(738\) 3.59157e17 0.0818310
\(739\) −4.30855e18 −0.973067 −0.486534 0.873662i \(-0.661739\pi\)
−0.486534 + 0.873662i \(0.661739\pi\)
\(740\) 4.42198e18 0.989944
\(741\) 4.28519e18 0.950936
\(742\) 2.23911e18 0.492550
\(743\) −4.35573e17 −0.0949804 −0.0474902 0.998872i \(-0.515122\pi\)
−0.0474902 + 0.998872i \(0.515122\pi\)
\(744\) −7.60020e17 −0.164286
\(745\) 8.14009e18 1.74427
\(746\) −5.96729e18 −1.26758
\(747\) −1.89238e18 −0.398496
\(748\) −9.48930e16 −0.0198095
\(749\) 1.44061e18 0.298135
\(750\) −1.91324e18 −0.392528
\(751\) 4.25348e18 0.865137 0.432569 0.901601i \(-0.357607\pi\)
0.432569 + 0.901601i \(0.357607\pi\)
\(752\) 1.60983e17 0.0324612
\(753\) −5.07686e18 −1.01491
\(754\) −1.42498e18 −0.282421
\(755\) −6.58415e17 −0.129373
\(756\) 5.04646e17 0.0983095
\(757\) 6.16432e18 1.19059 0.595294 0.803508i \(-0.297036\pi\)
0.595294 + 0.803508i \(0.297036\pi\)
\(758\) −9.69565e17 −0.185664
\(759\) 3.30186e17 0.0626883
\(760\) −4.60505e18 −0.866854
\(761\) 6.30534e18 1.17681 0.588407 0.808565i \(-0.299755\pi\)
0.588407 + 0.808565i \(0.299755\pi\)
\(762\) 1.12175e18 0.207581
\(763\) 9.28961e18 1.70446
\(764\) 4.92152e18 0.895349
\(765\) 8.83113e16 0.0159300
\(766\) −5.05690e18 −0.904476
\(767\) −1.28168e18 −0.227306
\(768\) 3.37346e18 0.593237
\(769\) 3.40289e17 0.0593371 0.0296686 0.999560i \(-0.490555\pi\)
0.0296686 + 0.999560i \(0.490555\pi\)
\(770\) −1.80283e18 −0.311721
\(771\) 6.00539e17 0.102965
\(772\) −5.00950e18 −0.851691
\(773\) 9.50368e18 1.60223 0.801115 0.598510i \(-0.204240\pi\)
0.801115 + 0.598510i \(0.204240\pi\)
\(774\) 6.72435e17 0.112418
\(775\) −3.04851e17 −0.0505390
\(776\) −1.48233e18 −0.243693
\(777\) 5.58324e18 0.910228
\(778\) −2.05168e17 −0.0331697
\(779\) 2.27034e18 0.363997
\(780\) 3.41664e18 0.543231
\(781\) −6.23294e17 −0.0982792
\(782\) 3.69830e16 0.00578307
\(783\) −3.15510e17 −0.0489285
\(784\) 8.65276e16 0.0133076
\(785\) −3.82983e18 −0.584153
\(786\) −1.32414e18 −0.200302
\(787\) −8.58472e16 −0.0128793 −0.00643963 0.999979i \(-0.502050\pi\)
−0.00643963 + 0.999979i \(0.502050\pi\)
\(788\) 1.50561e18 0.224023
\(789\) 4.69331e17 0.0692594
\(790\) 2.84711e17 0.0416704
\(791\) 2.06569e18 0.299859
\(792\) 1.48160e18 0.213312
\(793\) −1.72651e18 −0.246543
\(794\) 5.03332e17 0.0712888
\(795\) 3.35653e18 0.471525
\(796\) 1.12793e18 0.157162
\(797\) −1.29548e18 −0.179040 −0.0895200 0.995985i \(-0.528533\pi\)
−0.0895200 + 0.995985i \(0.528533\pi\)
\(798\) −2.16948e18 −0.297397
\(799\) −2.49448e17 −0.0339176
\(800\) 1.31353e18 0.177156
\(801\) −3.44198e18 −0.460465
\(802\) −5.26495e18 −0.698651
\(803\) −2.50234e18 −0.329379
\(804\) 2.30270e18 0.300658
\(805\) −1.03315e18 −0.133810
\(806\) −2.42415e18 −0.311445
\(807\) −2.33132e18 −0.297114
\(808\) −1.07641e19 −1.36083
\(809\) 2.98865e18 0.374809 0.187404 0.982283i \(-0.439993\pi\)
0.187404 + 0.982283i \(0.439993\pi\)
\(810\) −5.14474e17 −0.0640046
\(811\) −5.04909e17 −0.0623129 −0.0311564 0.999515i \(-0.509919\pi\)
−0.0311564 + 0.999515i \(0.509919\pi\)
\(812\) −1.06080e18 −0.129874
\(813\) 2.96029e18 0.359539
\(814\) 6.11619e18 0.736924
\(815\) −3.08538e18 −0.368794
\(816\) 1.29827e16 0.00153949
\(817\) 4.25067e18 0.500051
\(818\) −2.19848e17 −0.0256582
\(819\) 4.31389e18 0.499487
\(820\) 1.81018e18 0.207937
\(821\) −1.73695e18 −0.197951 −0.0989756 0.995090i \(-0.531557\pi\)
−0.0989756 + 0.995090i \(0.531557\pi\)
\(822\) −3.40439e18 −0.384922
\(823\) −3.82731e18 −0.429334 −0.214667 0.976687i \(-0.568867\pi\)
−0.214667 + 0.976687i \(0.568867\pi\)
\(824\) −1.94111e18 −0.216034
\(825\) 5.94281e17 0.0656208
\(826\) 6.48884e17 0.0710881
\(827\) −4.13981e18 −0.449982 −0.224991 0.974361i \(-0.572235\pi\)
−0.224991 + 0.974361i \(0.572235\pi\)
\(828\) 3.16802e17 0.0341658
\(829\) 1.10335e19 1.18061 0.590307 0.807179i \(-0.299007\pi\)
0.590307 + 0.807179i \(0.299007\pi\)
\(830\) 6.48644e18 0.688650
\(831\) 7.78056e18 0.819604
\(832\) 1.12890e19 1.17992
\(833\) −1.34077e17 −0.0139047
\(834\) −4.85461e18 −0.499545
\(835\) −1.23442e18 −0.126038
\(836\) 3.49453e18 0.354037
\(837\) −5.36738e17 −0.0539569
\(838\) −3.32841e18 −0.332009
\(839\) 2.68075e18 0.265340 0.132670 0.991160i \(-0.457645\pi\)
0.132670 + 0.991160i \(0.457645\pi\)
\(840\) −4.63590e18 −0.455322
\(841\) −9.59740e18 −0.935362
\(842\) 2.09926e17 0.0203020
\(843\) −1.93577e18 −0.185769
\(844\) 9.63823e18 0.917849
\(845\) 1.96257e19 1.85463
\(846\) 1.45321e18 0.136276
\(847\) −5.55597e18 −0.517032
\(848\) 4.93445e17 0.0455686
\(849\) 2.04707e18 0.187600
\(850\) 6.65635e16 0.00605359
\(851\) 3.50500e18 0.316334
\(852\) −5.98031e17 −0.0535632
\(853\) 2.66716e18 0.237072 0.118536 0.992950i \(-0.462180\pi\)
0.118536 + 0.992950i \(0.462180\pi\)
\(854\) 8.74086e17 0.0771042
\(855\) −3.25216e18 −0.284703
\(856\) 4.05806e18 0.352565
\(857\) 1.46804e19 1.26580 0.632898 0.774235i \(-0.281865\pi\)
0.632898 + 0.774235i \(0.281865\pi\)
\(858\) 4.72567e18 0.404386
\(859\) −7.69268e18 −0.653314 −0.326657 0.945143i \(-0.605922\pi\)
−0.326657 + 0.945143i \(0.605922\pi\)
\(860\) 3.38913e18 0.285659
\(861\) 2.28555e18 0.191192
\(862\) 5.12060e18 0.425132
\(863\) 4.13923e17 0.0341075 0.0170537 0.999855i \(-0.494571\pi\)
0.0170537 + 0.999855i \(0.494571\pi\)
\(864\) 2.31268e18 0.189137
\(865\) −1.04755e19 −0.850294
\(866\) 1.77084e17 0.0142664
\(867\) 7.20032e18 0.575742
\(868\) −1.80461e18 −0.143221
\(869\) −5.79038e17 −0.0456119
\(870\) 1.08146e18 0.0845545
\(871\) 1.96843e19 1.52757
\(872\) 2.61680e19 2.01564
\(873\) −1.04684e18 −0.0800366
\(874\) −1.36194e18 −0.103355
\(875\) −1.21752e19 −0.917114
\(876\) −2.40091e18 −0.179515
\(877\) −6.24713e18 −0.463642 −0.231821 0.972758i \(-0.574468\pi\)
−0.231821 + 0.972758i \(0.574468\pi\)
\(878\) −2.97700e18 −0.219313
\(879\) −8.19580e18 −0.599327
\(880\) −3.97300e17 −0.0288391
\(881\) −3.31160e18 −0.238613 −0.119307 0.992857i \(-0.538067\pi\)
−0.119307 + 0.992857i \(0.538067\pi\)
\(882\) 7.81091e17 0.0558670
\(883\) −2.40266e19 −1.70588 −0.852939 0.522011i \(-0.825182\pi\)
−0.852939 + 0.522011i \(0.825182\pi\)
\(884\) −7.78299e17 −0.0548538
\(885\) 9.72709e17 0.0680537
\(886\) 1.95506e18 0.135781
\(887\) −1.50333e19 −1.03646 −0.518229 0.855242i \(-0.673409\pi\)
−0.518229 + 0.855242i \(0.673409\pi\)
\(888\) 1.57275e19 1.07640
\(889\) 7.13841e18 0.484998
\(890\) 1.17979e19 0.795740
\(891\) 1.04633e18 0.0700587
\(892\) 4.88040e18 0.324403
\(893\) 9.18617e18 0.606178
\(894\) 1.08025e19 0.707669
\(895\) 5.89044e18 0.383088
\(896\) 7.34841e18 0.474451
\(897\) 2.70814e18 0.173588
\(898\) −2.76911e18 −0.176215
\(899\) 1.12826e18 0.0712808
\(900\) 5.70194e17 0.0357640
\(901\) −7.64606e17 −0.0476131
\(902\) 2.50372e18 0.154790
\(903\) 4.27915e18 0.262656
\(904\) 5.81886e18 0.354603
\(905\) −2.34462e18 −0.141859
\(906\) −8.73765e17 −0.0524882
\(907\) −2.39524e19 −1.42857 −0.714287 0.699853i \(-0.753249\pi\)
−0.714287 + 0.699853i \(0.753249\pi\)
\(908\) 1.53339e19 0.908018
\(909\) −7.60177e18 −0.446940
\(910\) −1.47866e19 −0.863175
\(911\) 2.80901e19 1.62811 0.814057 0.580786i \(-0.197255\pi\)
0.814057 + 0.580786i \(0.197255\pi\)
\(912\) −4.78101e17 −0.0275139
\(913\) −1.31920e19 −0.753788
\(914\) −2.04954e19 −1.16280
\(915\) 1.31030e18 0.0738130
\(916\) 8.80073e18 0.492264
\(917\) −8.42635e18 −0.467992
\(918\) 1.17195e17 0.00646299
\(919\) −2.16751e19 −1.18689 −0.593444 0.804875i \(-0.702232\pi\)
−0.593444 + 0.804875i \(0.702232\pi\)
\(920\) −2.91028e18 −0.158239
\(921\) −1.59882e19 −0.863202
\(922\) 1.86817e19 1.00153
\(923\) −5.11217e18 −0.272141
\(924\) 3.51794e18 0.185961
\(925\) 6.30844e18 0.331132
\(926\) −8.03731e18 −0.418928
\(927\) −1.37084e18 −0.0709526
\(928\) −4.86142e18 −0.249862
\(929\) 1.63331e19 0.833618 0.416809 0.908994i \(-0.363148\pi\)
0.416809 + 0.908994i \(0.363148\pi\)
\(930\) 1.83976e18 0.0932442
\(931\) 4.93752e18 0.248505
\(932\) −8.39255e18 −0.419460
\(933\) 1.76684e19 0.876933
\(934\) 3.98890e18 0.196607
\(935\) 6.15627e17 0.0301330
\(936\) 1.21518e19 0.590676
\(937\) 1.37811e19 0.665237 0.332618 0.943062i \(-0.392068\pi\)
0.332618 + 0.943062i \(0.392068\pi\)
\(938\) −9.96565e18 −0.477735
\(939\) −1.21345e19 −0.577690
\(940\) 7.32427e18 0.346285
\(941\) 9.47490e18 0.444879 0.222440 0.974946i \(-0.428598\pi\)
0.222440 + 0.974946i \(0.428598\pi\)
\(942\) −5.08246e18 −0.236997
\(943\) 1.43480e18 0.0664457
\(944\) 1.42998e17 0.00657677
\(945\) −3.27394e18 −0.149542
\(946\) 4.68762e18 0.212647
\(947\) −2.78282e18 −0.125375 −0.0626874 0.998033i \(-0.519967\pi\)
−0.0626874 + 0.998033i \(0.519967\pi\)
\(948\) −5.55568e17 −0.0248590
\(949\) −2.05238e19 −0.912070
\(950\) −2.45127e18 −0.108190
\(951\) −2.02956e19 −0.889667
\(952\) 1.05604e18 0.0459770
\(953\) −1.09628e19 −0.474041 −0.237021 0.971505i \(-0.576171\pi\)
−0.237021 + 0.971505i \(0.576171\pi\)
\(954\) 4.45436e18 0.191303
\(955\) −3.19288e19 −1.36195
\(956\) 1.65428e19 0.700862
\(957\) −2.19945e18 −0.0925523
\(958\) −1.06670e19 −0.445827
\(959\) −2.16644e19 −0.899344
\(960\) −8.56752e18 −0.353258
\(961\) −2.24982e19 −0.921394
\(962\) 5.01642e19 2.04059
\(963\) 2.86586e18 0.115794
\(964\) −1.39251e19 −0.558854
\(965\) 3.24996e19 1.29554
\(966\) −1.37106e18 −0.0542882
\(967\) 5.00459e19 1.96832 0.984162 0.177271i \(-0.0567268\pi\)
0.984162 + 0.177271i \(0.0567268\pi\)
\(968\) −1.56507e19 −0.611425
\(969\) 7.40830e17 0.0287484
\(970\) 3.58822e18 0.138313
\(971\) −1.37541e19 −0.526633 −0.263316 0.964710i \(-0.584816\pi\)
−0.263316 + 0.964710i \(0.584816\pi\)
\(972\) 1.00392e18 0.0381827
\(973\) −3.08931e19 −1.16715
\(974\) −1.55804e19 −0.584716
\(975\) 4.87421e18 0.181708
\(976\) 1.92627e17 0.00713336
\(977\) 2.88788e19 1.06234 0.531172 0.847264i \(-0.321752\pi\)
0.531172 + 0.847264i \(0.321752\pi\)
\(978\) −4.09452e18 −0.149624
\(979\) −2.39944e19 −0.871008
\(980\) 3.93676e18 0.141961
\(981\) 1.84802e19 0.662001
\(982\) −3.32817e19 −1.18435
\(983\) 1.53615e19 0.543044 0.271522 0.962432i \(-0.412473\pi\)
0.271522 + 0.962432i \(0.412473\pi\)
\(984\) 6.43820e18 0.226098
\(985\) −9.76779e18 −0.340769
\(986\) −2.46354e17 −0.00853805
\(987\) 9.24771e18 0.318400
\(988\) 2.86617e19 0.980351
\(989\) 2.68633e18 0.0912816
\(990\) −3.58646e18 −0.121070
\(991\) −2.66515e19 −0.893806 −0.446903 0.894582i \(-0.647473\pi\)
−0.446903 + 0.894582i \(0.647473\pi\)
\(992\) −8.27012e18 −0.275541
\(993\) 2.46519e19 0.815981
\(994\) 2.58816e18 0.0851099
\(995\) −7.31756e18 −0.239065
\(996\) −1.26573e19 −0.410822
\(997\) −1.11779e19 −0.360446 −0.180223 0.983626i \(-0.557682\pi\)
−0.180223 + 0.983626i \(0.557682\pi\)
\(998\) 6.50061e18 0.208260
\(999\) 1.11070e19 0.353526
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.14.a.b.1.13 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.b.1.13 31 1.1 even 1 trivial